Jupiter exerts the third biggest force on Earth, preceded by the Sun and the Moon. And it is a very poor third. Jupiter’s gravitational force on the Earth is greater than that of all the other planets combined. Simple - use Newton’s Law of Gravitation, and use relative masses and distances in Astronomical Units to keep it simple, and you will get the same scale differences.
As for Mars losing its atmosphere, I believe it was more due to the core solidifying. Loss of the core’s liquid state resulted in the loss of its magnetic field, shielding it from the solar wind. The solar wind then ablated away the atmosphere, aided by Mar’s lower gravity.